Force Field Potential Functions

The potential functions may be divided into bonded terms, which give the energy contained in the internal degrees of freedom, and non-bonded terms, which describe interactions between molecules.

Force Field Potential Functions

atoms

ticselectrostaatoms

svanderWaaltorsionsanglesbonds

rpot VVVVVE

Potentials between bonded atoms= zero for most water models

Potentials between non-bonded atoms

Total potential Energy, Epot or Vtot

jiRij

ij

jiticElectrosta R

qqV

4

Electrostatics and Solvation

jiRij

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VElectrostatic =qiq jεrRij

Here r is the relative electric permitivity also known as the “dielectric constant”.

When other molecules exist between the charges, they may weaken the electrostatic interaction depending on the extent of their polarity. The more polar the intervening molecules the more they screen the two charges from each other.

This effect is very important for water because water is very polar.

Charge screening can be explicitly modeled if individual waters are present, or it can be approximated implicitly using the dielectric constant of the solvent.

For example, water (very polar, dipole = 1.85D) has a dielectric constant of 80 while n-butanol (less polar, dipole = 1.63D) has a dielectric constant of 18, at 20 °C

0 20 40 60 80 100 120

-0.100

-0.090

-0.080

-0.070

-0.060

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

Gas Phasewater

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VElectrostatic =qiq jεrRij

Rij

Dielectric (r = 80)

Dielectric (r = 1)

Effect of Dielectric Constant on Electrostatic Interaction Energy

Employing a large dielectric constant effectively eliminates electrostatic interactions When is this reasonable? Only when the charges are far apart

Potential energy functions for atomic-level simulations of water and organic and biomolecular systemsWilliam L. Jorgensen * and Julian Tirado-Rives PNAS May 10, 2005 vol. 102 no. 19 6665–6670

Fig. 1. Computed (OPLS-AA) and experimental results for liquid densities (Left), heats of vaporization (Middle), and free energies of hydration (Right) at 25°C and 1 atm.

Fig. 2. Computed and experimental results for the density (gcm3) of liquid water vs. temperature ata pressure of 1 atm.

Coming up: Effects of water models on Biomolecular Structure

1) Explicit Water Models Affect the Specific Solvation and Dynamics of Unfolded Peptides While the Conformational Behavior and Flexibility of Folded Peptides Remain IntactPetra Florov, Petr Sklenovsk, Pavel Ban, and Michal OtyepkaJ. Chem. Theory Comput., 2010, 6, 3569–3579

2) On the role of water models in quantifying the standard binding free energy of highly conserved water molecules in proteins: the case of Concanavalin A. Elisa Fadda and Robert J. Woods J. Chem. Theory Comput. (2011). In Press. DOI: 10.1021/ct200404z.